RANDOM VARIABLES
A random variable X is a function that assigns numbers to any possible outcome of a random experiment
Unidimensional random variables
Unidimensional random variables
Explore the concept of unidimensional random variables, their classification into discrete and continuous types, and how they are used in probability and statistics.
Cumulative distribution function
The CDF gives the probability that a random variable takes a value less than or equal to a given point, providing a complete picture of its distribution.
Probability density function
The probability density function describes the relative likelihood of a continuous random variable taking values in a given range
Probability mass function
The probability mass function assigns a probability to each possible value of a discrete random variable
Bidimensional random variables
Bidimensional random variables
Bidimensional random variables describe the joint behavior of two variables simultaneously, through joint, marginal and conditional distributions.
Joint distribution function
The joint distribution function gives the probability that two random variables simultaneously take values below specified thresholds
Joint probability density function
The joint PDF describes the combined probability distribution of two continuous random variables simultaneously
Marginal probability density function
The marginal PDF gives the distribution of one variable by integrating out the other, collapsing the joint distribution onto a single axis